Is mathematics discovery or invention?  In other words, are the truths of mathematics true before anyone discovers them, or do they become true when we decide to call them true?  My impression is that most mathematicians believe as I do in the former alternative, that mathematics is discovery and not invention.  If it were not so, if it were in mathematicians’ power to confer upon or withhold from a proposition its “truth”, then mathematics would be an empty and uninteresting pursuit, like politics.  But I suspect that people who believe the contrary are more interested in politics than in mathematics.

If mathematical truths exist prior to their discovery, they must equally have existed before the Big Bang.  Evidently mathematical objects have a platonic reality, apart from the reality of material objects.  Yet the mere possibility of non-material reality is philosophically significant, and many people base their metaphysics on denying this possibility.

Since Galileo and Newton opened the eyes of the modern intellect to the world of matter, the fascination of studying it and finding ourselves able to learn about it and control it have turned our thoughts away from the contemplation of anything other than matter.  The modern tendency toward atheism stems from a disinclination to imagine that anything not made of matter might still have real existence.  The study of mathematics is an anodyne for this kind of blindness.  For anyone who realizes that mathematical objects have an existence wholly independent of the world of matter, the supposed implausibility of the theistic hypothesis falls to the ground.

The hypothesis that only matter exists not only fails to be inevitable, it is actually implausible in the light of quantum physics.  The physicists assure us that at the smallest level, matter behaves according to laws that are statistical rather than deterministic; that the exact behavior of fundamental particles is unpredictable in principle.  They imagine that the dethroning of causality is a matter of minor importance, since individual electrons are unimportant to our daily affairs and at the scale in which we live, statistical laws ensure that causality continues to operate.  But philosophically, to say that the behavior of an electron has no natural cause is to say that its cause is supernatural.  What quantum physics shows sounds much like what theology calls the immanence of God’s action in the world -- that at every moment, God maintains in being everything in the universe -- down to that last electron.

The Deists, soon after Newtonian physics arose, allowed God’s existence but rejected His action in the world -- God became the Divine Clockmaker.  Quantum physics utterly demolishes Deism, particularly in combination with the current ideas of chaos theory.  In a complex system, extremely small variations in the inputs can lead to large variations in the outputs.  This is demonstrable by means of computer simulations, which for all their shortcomings as far as predicting reality are concerned, can irrefutably provide us with information concerning the behavior of complex systems since the computer program itself is an example of such a system.  But if the universe is indeterminate at the smallest level, and small changes can lead over time to large changes, then it would be impossible in principle to predict, say, the providentially good weather on D-Day for the Allies from the state of the universe at the Big Bang.  But if an omniscient Being had control of the quantum fluctuations of every particle in the earth’s atmosphere for several months in advance, such good weather could be provided -- by an immanent God.

Questions, corrections, comments:  Send me e-mail at  markthom@flash.net